From c0501a1ff77f64d9d739dfe3281bc6265d7d2ad2 Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Tue, 12 Mar 2019 12:19:36 +1100 Subject: [PATCH] [spec] circular functions (sec & cosec) --- spec/circ.md | 27 +++++++++++++++++++++++++++ 1 file changed, 27 insertions(+) create mode 100644 spec/circ.md diff --git a/spec/circ.md b/spec/circ.md new file mode 100644 index 0000000..a119a4a --- /dev/null +++ b/spec/circ.md @@ -0,0 +1,27 @@ +# Circular functions + +## Reciprocal functions + +### Cosecant + +$$\mathrm{cosec} \Theta = {1 \over \sin \Theta} \vert \sin \Theta \ne 0$$ + +- **Domain** $= \mathbb{R} \ {n\pi : n \in \mathbb{Z}$ +- **Range** $= \mathbb{R} \ (-1, 1)$ +- **Turning points** at $\Theta = {{(2n + 1)\pi} \over 2} \vert n \in \mathbb{Z}$ +- **Asymptotes** at $\Theta = n\pi \vert n \in \math{Z}$ + + +### Secant + +$$\mathrm{sec} \Theta = {1 \over \cos \Theta} \vert \cos \Theta \ne =$$ + +- **Domain** $= \mathbbb{R} \ \{{{(2n + 1) \pi} \over 2 } : n \in \mathbb{Z}\}$ +- **Range** $= \mathbb{R} \ (-1, 1)$ +- **Turning points** at $\Theta n \pi \vert n \in \mathbb{Z}$ +- **Asymptotes** at $\Theta = {{(2n + 1) \pi} \over 2} \vert n \in \mathb{Z}$ + + +### Cotangent + +$$\mathrm{cot} \Theta = {{\cos \Theta} \over {\sin \Theta}}$$ -- 2.47.1